{VERSION 5 0 "IBM INTEL NT" "5.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 1 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 1 } {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Heading 1" -1 3 1 {CSTYLE "" -1 -1 "Times" 1 18 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }1 1 0 0 8 4 1 0 1 0 2 2 0 1 }{PSTYLE "Heading 2" -1 4 1 {CSTYLE "" -1 -1 "Times " 1 14 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }1 1 0 0 8 2 1 0 1 0 2 2 0 1 } {PSTYLE "Warning" -1 7 1 {CSTYLE "" -1 -1 "Courier" 1 10 0 0 255 1 2 2 2 2 2 1 1 1 3 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Diagnostic" -1 9 1 {CSTYLE "" -1 -1 "Courier" 1 10 64 128 64 1 2 2 2 2 2 1 1 1 3 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Output" -1 11 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 3 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Output" -1 12 1 {CSTYLE "" -1 -1 "Ti mes" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 3 0 0 0 0 1 0 1 0 2 2 0 1 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 13 "Cryptographie" }}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 4 " RSA" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 101 "p:=nextprime( 1789123456);\nq:=nextprime(1247894625);\nN:=p*q;\nm:=2^25+1;\nphi:=(p- 1)*(q-1);\nigcd(m,phi);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"pG\"+\" [B\"*y\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"qG\"+%\"NG\"4x)\\0+SxjKA" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"mG\")LWbL" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$phi G\"4!oJN'ptPEB#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 106 "coder:= proc(L)\nlocal i,S;\nS:=NU LL;\nfor i from 1 to nops(L) do\n S:=S,L[i]&^m mod N;\nod;\nRETURN([S ]);\nend:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "L:=[1,2,3,4,5,6,7,45,23,89,456,2,3] ;\nR:=coder(L);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"LG7/\"\"\"\"\"# \"\"$\"\"%\"\"&\"\"'\"\"(\"#X\"#B\"#*)\"$c%F'F(" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%\"RG7/\"\"\"\"4v!>l3B-e#4\"\"4Nldb%HYWF@\"3$*R#Gx)fM( H%\"3)z#ei2b3z]\"4(*)G$)>R%fP0\"\"3.mqg\"*\\^Rr\"4s$*GrOU*408\"3bj\\Qs bLy5\"4[cs7P%=Mh9\"4>p'G!*4;KA5F'F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 187 "decode r:= proc(L)\n#option trace;\nlocal i,S,k;\nS:=NULL;\nk:=Euclideetendu( m,phi)[2] mod phi;\n#if (k<0) then k:=k+N;fi;\nfor i from 1 to nops(L) do\n S:=S,L[i]&^k mod N;\nod;\nRETURN([S]);\nend:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "decoder(R);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7/\"\"\"\"\"#\"\" $\"\"%\"\"&\"\"'\"\"(\"#X\"#B\"#*)\"$c%F%F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "ifac tor(phi);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*,)-%!G6#\"\"#\"\"&\"\"\" -F&6#F)F*-F&6#\"#BF*-F&6#\")tSc8F*-F&6#\")(3GZ%F*" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 16 "ifactor(2^25+1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#**-%!G6#\"\"$\"\"\"-F%6#\"#6F(-F%6#\"$^#F(-F%6#\"%^SF( " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 19 " log arithme discret" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "with(numt heory);" }}{PARA 7 "" 1 "" {TEXT -1 41 "Warning, the name phi has been redefined\n" }}{PARA 7 "" 1 "" {TEXT -1 69 "Warning, the protected na me order has been redefined and unprotected\n" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#7P%&GIgcdG%)bigomegaG%&cfracG%)cfracpolG%+cyclotomicG%) divisorsG%)factorEQG%*factorsetG%'fermatG%)imagunitG%&indexG%/integral _basisG%)invcfracG%'invphiG%*issqrfreeG%'jacobiG%*kroneckerG%'lambdaG% )legendreG%)mcombineG%)mersenneG%*minkowskiG%(mipolysG%%mlogG%'mobiusG %&mrootG%&msqrtG%)nearestpG%*nthconverG%)nthdenomG%)nthnumerG%'nthpowG %&orderG%)pdexpandG%$phiG%#piG%*pprimrootG%)primrootG%(quadresG%+roots unityG%*safeprimeG%&sigmaG%*sq2factorG%(sum2sqrG%$tauG%%thueG" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 94 "logdiscret:=proc(n,g,N)\nlocal i;\ni:=1;\nwhile (g& ^i mod N) <> n do i:= i+1;\nod;\nRETURN(i);\nend:" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "N:=nextprime(14789);\n primroot(N*N);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"NG\"&(z9" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "logdiscret(48,2,N);" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#\"&q=\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "2&^11870 mod N ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#[" }}}}}{SECT 1 {PARA 3 "" 0 " " {TEXT -1 11 "Congruences" }}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 22 " ex ponentiation rapide" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 226 "exponentiation:=proc(a,m,j) \n#option trace;\nlocal x,y,n;\nx:=a;\ny:=1;\nn:=m;\n\nwhile (n<>1) do \n if (n mod 2 <>1) then \n n:=n/2;\n else \n y:=y*x mod j ;\n n:=(n-1)/2;\n fi;\n x:=x^2 mod j;\nod;\n\nRETURN (y*x mod j) ;\nend:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 57 "st:=time():\nexp onentiation (23244,121232,123);\ntime()-st;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#U" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"\"!F$" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "st:=time():\n23244&^121232 m od 123;\ntime()-st;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#U" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"\"!F$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "st:=time():\n23244^121232 mod 123;\ntime()-st;" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#\"#U" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#$\"%9G!\"$" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 29 " th\351or\350m e des restes chinois" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 207 "Euclideetendu:= proc(a,b)\n local q,r,wp,wn,w;\nwp:=(a,1,0);\nwn:=(b,0,1);\nr:=irem(a,b,'q');\nwhi le r<>0 do\n w:=(r,wp[2]-q*wn[2],wp[3]-q*wn[3]);\n wp:=wn;\n wn:=w; \n r:=irem(wp[1],wn[1],'q');\nod;\nRETURN(w);\nend:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "Euclideetendu(58,23);" }}{PARA 11 "" 1 " " {XPPMATH 20 "6%\"\"\"\"\"#!\"&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 219 "chinois:=proc(X,M)\n#option trace;\nlocal i,E,r,s,n; \n\nr:=nops(X);\nn:=product( M[i], i=1..r );\nE:=array(1..r);\ns:=0;\n \nfor i from 1 to r do\n E[i]:=1-Euclideetendu(M[i],n/M[i])[2]*M[i]; \n s:=s+E[i]*X[i];\nod;\nRETURN(s);\nend:" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "chino is([1,2,3,4],[5,7,9,11]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"%'>&" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "5196 mod 5; 5196 mod 7; 5 196 mod 9; 5196 mod 11;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"\"" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"%" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 9 "Primalit\351" }}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 25 " un test de non primalit\351" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 207 "test:=proc(n,k)\n#option trace;\nl ocal j,a ;\na:=2;\nfor j from 2 to k do\n if (igcd(j,n)<>1) then \n \+ break;\n fi;\n if ((j^(n-1) mod n )<> 1) then RETURN('compos\351 ');\n fi;\nod;\nRETURN('pseudo-premier');\nend:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "test(24551,7);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&%'pseudoG\"\"\"%(premierG!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "test(561,7);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&%'p seudoG\"\"\"%(premierG!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "isprime(24551);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%%trueG" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "test(1729,7);" }}{PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 14 "isprime(1729);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&%'pseudoG\"\"\"%(premierG!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%&falseG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 4 "" 0 " " {TEXT -1 27 " le crit\350re de Miller-Rabin" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 369 "t est2:=proc(n,k)\noption trace;\nlocal j,a,s,t,u,i,cpt;\ns:=0;\na:=2;\n cpt:=500;\nu:=n-1;\nwhile (irem(u,2)<>1) do\n s:=s+1;\n u:=u/2;\nod; \nt:=(n-1)/2^s;\nfor j from 1 to k do\n for i from 0 to (s-1) do\n \+ if ((j^t mod n )<> 1 and (j^(2^i*t) mod n )<> n-1) then cpt:=cpt+1; \n fi;\n od;\nif cpt=500+s-1 then RETURN('compos\351');fi;\ncpt:= 5000;\nod;\nRETURN('pseudo-premier');\nend:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "test2(1729,10);" }}{PARA 9 "" 1 "" {TEXT -1 33 "\{ --> enter test2, args = 1729, 10" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>% \"sG\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"aG\"\"#" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#>%$cptG\"$+&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6# >%\"uG\"%G<" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"sG\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"uG\"$k)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"sG\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"uG\"$K%" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"sG\"\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"uG\"$;#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"sG\" \"%" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"uG\"$3\"" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#>%\"sG\"\"&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"uG \"#a" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"sG\"\"'" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#>%\"uG\"#F" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"tG \"#F" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$cptG\"%+]" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$cptG\"%,]" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$c ptG\"%-]" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$cptG\"%.]" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#>%$cptG\"%/]" }}{PARA 11 "" 1 "" {XPPMATH 20 "6# >%$cptG\"%0]" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$cptG\"%1]" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$cptG\"%+]" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$cptG\"%,]" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$cptG\"%-]" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%$cptG\"%.]" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$cptG\"%/]" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$cptG \"%0]" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$cptG\"%1]" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$cptG\"%+]" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>% $cptG\"%,]" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$cptG\"%-]" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$cptG\"%.]" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$cptG\"%/]" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$cptG\"%0]" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%$cptG\"%1]" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$cptG\"%+]" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$cptG \"%,]" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$cptG\"%-]" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$cptG\"%.]" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>% $cptG\"%/]" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$cptG\"%0]" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$cptG\"%1]" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$cptG\"%+]" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$cptG\"%,]" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%$cptG\"%-]" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$cptG\"%.]" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$cptG \"%/]" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$cptG\"%0]" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$cptG\"%1]" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>% $cptG\"%+]" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$cptG\"%,]" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$cptG\"%-]" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$cptG\"%.]" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$cptG\"%/]" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%$cptG\"%0]" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$cptG\"%1]" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$cptG \"%+]" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$cptG\"%,]" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$cptG\"%-]" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>% $cptG\"%.]" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$cptG\"%/]" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$cptG\"%0]" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$cptG\"%1]" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$cptG\"%+]" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%$cptG\"%+]" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$cptG\"%,]" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$cptG \"%-]" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$cptG\"%.]" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$cptG\"%/]" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>% $cptG\"%0]" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$cptG\"%+]" }}{PARA 9 "" 1 "" {TEXT -1 51 "<-- exit test2 (now at top level) = pseudo-premie r\}" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&%'pseudoG\"\"\"%(premierG!\" \"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "test2(1127507,10);" } }{PARA 9 "" 1 "" {TEXT -1 36 "\{--> enter test2, args = 1127507, 10" } }{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"sG\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"aG\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$cptG \"$+&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"uG\"(1v7\"" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#>%\"sG\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6# >%\"uG\"'`Pc" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"tG\"'`Pc" }}{PARA 9 "" 1 "" {TEXT -1 44 "<-- exit test2 (now at top level) = compos\351 \}" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%(compos|dyG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "nextprime(1127465);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"(2v7\"" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 26 " la \+ m\351thode pho de Pollard" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 204 "pollard:=proc(n,x0)\nlocal x,y,g;\ny:=x0;\nx:=x0;\ng:=1;\nwhile ( g=1) do\n x:=x^2+1 mod n;\n y:=(y^2+1)^2+1 mod n;\n g:=igcd(x-y,n); \nod;\nif (g=n) then RETURN(\"mauvais choix de x0\") else RETURN(g,n/g );\nfi;\nend:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "pollard(349703,3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$\"$\\\"\"%ZB" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 73 "nextprime(954)*nextprime(24954)*nextprime(46954);\nif actor(1133687030173);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\".t,.(oL6" } }{PARA 11 "" 1 "" {XPPMATH 20 "6#*(-%!G6#\"$n*\"\"\"-F%6#\"&n\\#F(-F%6 #\"&dp%F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "pollard(113368 7030173,2);\npollard(1133687030173,6);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$\"$n*\"+>aPs6" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$\"&dp%\")*3VT# " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}}}{MARK "1" 0 } {VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }